/**
 * Calculate fibonacci number at specific position using closed form function (Binet's formula).
 * @see: https://en.wikipedia.org/wiki/Fibonacci_number#Closed-form_expression
 *
 * parameter:  {number} position - Position number of fibonacci sequence (must be number from 1 to 75).
 * @return {number}
 */
export default function fibonacciClosedForm( position ) {
  const topMaxValidPosition = 70;

  // Check that position is valid.
  if ( position < 1 || position > topMaxValidPosition ) {
    throw new Error( `Can't handle position smaller than 1 or greater than ${topMaxValidPosition}` );
  }

  // Calculate √5 to re-use it in further formulas.
  const sqrt5 = Math.sqrt( 5 );
  // Calculate φ constant (≈ 1.61803).
  const phi = ( 1 + sqrt5 ) / 2;

  // Calculate fibonacci number using Binet's formula.
  return Math.floor( ( phi ** position ) / sqrt5 + 0.5 );
}
